Abstract.
We prove that the functions \(\Phi (x) = [\Gamma (x + 1)]^{1/x} (1 + 1/x)^x /x\) and \(\log \Phi (x)\) are Stieltjes transforms.
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Berg, C. Integral Representation of Some Functions Related to the Gamma Function. MedJM 1, 433–439 (2004). https://doi.org/10.1007/s00009-004-0022-6
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DOI: https://doi.org/10.1007/s00009-004-0022-6